Looking at the internet, it looks like Sweden supports 300 days of unemployment benefits that max out at 1200 SEK/day (about $115 US). In the US, one can receive up to 210 days of unemployment with a max benefit of $145/week.
So yes, there is unemployment insurance in the US, and it pays almost 30% more than in Sweden. There is a HUGE gotcha, though, and that's the cost of health insurance. Unless the former employer is subsidizing, that costs about $400-700/month. There are, in general, far fewer social welfare services to rely on as well.
I think you just compared a daily rate to a weekly rate, if I'm reading correctly? Which would make the US rates very small in comparison, especially combined with health insurance as you describe.
So yes, there is unemployment insurance in the US, and it pays almost 30% more than in Sweden. There is a HUGE gotcha, though, and that's the cost of health insurance. Unless the former employer is subsidizing, that costs about $400-700/month. There are, in general, far fewer social welfare services to rely on as well.